Best Constants in Young’s Inequality, Its Converse, and Its Generalization to More than Three Functions

Herm Jan Brascamp and Elliott H. Lieb
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Herm Jan Brascamp: Princeton University, Department of Physics
Elliott H. Lieb: Princeton University, Department of Mathematics and Physics

A chapter in Inequalities, 2002, pp 417-439 from Springer

Abstract: Abstract The best possible constant Dmt in the inequality | ∬ dx dyf(x)g(x —y) h(y)| |, 1/p + llq+ 1/t = 2, is determined; the equality is reached if /, g, and h are appropriate Gaussians. The same is shown to be true for the converse inequality (0

Keywords: Equality Sign; Good Constant; Converse Inequality; Rearrangement Inequality; Schwarz Symmetrization (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55925-9_35

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DOI: 10.1007/978-3-642-55925-9_35

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